PHYSICAL MATHEMATICS SEMINAR
TOPIC: ANOMALOUS DIFFUSION AND RELAXATION:
A FRACTIONAL FOKKER-PLANCK EQUATION APPROACH
SPEAKER: ELI BARKAI
Department of Chemistry
Massachusetts Institute of Technology
ABSTRACT:
Fractional calculus is an old field of mathematical analysis
which deals with integrals and derivatives of arbitrary order.
Recently fractional diffusion equations and fractional Fokker--Planck
equations were introduced to describe anomalous diffusion and relaxation.
The stochastic foundation of these fractional equations is the well-known
continuous time random walk, which is known to describe certain types of
anomalous processes.
The fractional diffusion equations describe the asymptotic behaviors of
these random walks. The fractional Fokker-Planck equations describe such
anomalous behavior under the combined influence of an external force field
and thermal heat bath. These equations are compatible with the
generalized Einstein relation (linear response theory) and their
stationary solution is the Boltzmann equilibrium. Relaxation of modes is
shown to follow a Mittag-Leffler decay (as observed previously in several
physical systems). We discuss the derivation, domain of validity and
applications of these fractional equations and show that this simple
approach can be used for the phenomenological description of certain types
of complicated transport phenomena.
DATE: TUESDAY, APRIL 3, 2001
TIME: 2:30 PM
LOCATION: Building 2, Room 338
Refreshments will be served at 3:30 PM in Room 2-349
Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA 02139